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arXiv · 2011.12925

On the global well-posedness for the periodic quintic nonlinear Schr\"odinger equation

Xueying Yu·Haitian Yue
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Abstract

In this paper, we consider the initial value problem for the quintic, defocusing nonlinear Schr\"odinger equation on $\Bbb T^2$ with general data in the critical Sobolev space $H^{\frac{1}{2}} (\Bbb T^2)$. We show that if a solution remains bounded in $H^{\frac{1}{2}} (\Bbb T^2)$ in its maximal interval of existence, then the solution is globally well-posed in $\Bbb T^2$.

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Xueying Yu, Haitian Yue. 2020-11-25. On the global well-posedness for the periodic quintic nonlinear Schr\"odinger equation. https://doi.org/10.1137/22m1531063

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